Projected range straggling

An estimate of AR ia alloys can be made usiug the empirical expression (12) of equation 10 where the average alloy reduced energy, is defined by equation 11, where C (i = 1, 2,... , n) is the elemental atomic fraction of the /th element, and is the elemental reduced energy defined iu equation 3. Using this formulation, the projected range straggling iu compounds can be calculated to within 20%. 

Gaussian-shaped depth profiles of P with three parameters of maximum concentration (Cmax), projected range (Rp) and range straggling (ARp). The energy loss (dE/dx) and energy straggling ( 2 square root of the variance) of the a beam in the Si layer were taken into account ... 

Fig. 6.4. Relationship between range, R, projected range, Rv, and range straggling, ARp, as functions of mass ratio, M2/Mh The range straggling, AR, is in the direction of the incident ion, and ARPJ, is perpendicular to the incident ion. Dashed lines, m = 1/3 solid lines, m = 1/2 (Winterbon et al. 1970)...

Figure 2 shows the reference coordinates and nomenclature of this geometry. Theoretical calculations of the projected range and straggle for various dopants and substrates have been calculated and shown in graphical form (4, 21-26). Some common dopant ions for silicon and gallium arsenide are shown in Figures 3, 4, 5, and 6. 

Stepwise creation of Gaussian implantation profiles, where the projected ranges are calculated with the stopping powers given by Kalbitzer [85] and convoluted with a width due to straggling. 

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